docs: def pointplot(df, projection=None,
                hue=None, categorical=False, scheme=None, k=5, cmap='Set1', vmin=None, vmax=None,
                scale=None, limits=(0.5, 2), scale_func=None,
                legend=False, legend_values=None, legend_labels=None, legend_kwargs=None, legend_var=None,
                figsize=(8, 6), extent=None, ax=None, **kwargs):
      """
      Geospatial scatter plot.
  
      Parameters
      ----------
      df : GeoDataFrame
          The data being plotted.
      projection : geoplot.crs object instance, optional
          A geographic projection. For more information refer to `the tutorial page on projections
          <https://nbviewer.jupyter.org/github/ResidentMario/geoplot/blob/master/notebooks/tutorials/Projections.ipynb>`_.
      hue : None, Series, GeoSeries, iterable, or str, optional
          Applies a colormap to the output points.
      categorical : boolean, optional
          Set to ``True`` if ``hue`` references a categorical variable, and ``False`` (the default) otherwise. Ignored
          if ``hue`` is left unspecified.
      scheme : None or {"quantiles"|"equal_interval"|"fisher_jenks"}, optional
          Controls how the colormap bin edges are determined. Ignored if ``hue`` is left unspecified.
      k : int or None, optional
          Ignored if ``hue`` is left unspecified. Otherwise, if ``categorical`` is False, controls how many colors to
          use (5 is the default). If set to ``None``, a continuous colormap will be used.
      cmap : matplotlib color, optional
          The `matplotlib colormap <http://matplotlib.org/examples/color/colormaps_reference.html>`_ to be used.
          Ignored if ``hue`` is left unspecified.
      vmin : float, optional
          Values below this level will be colored the same threshold value. Defaults to the dataset minimum. Ignored
          if ``hue`` is left unspecified.
      vmax : float, optional
          Values above this level will be colored the same threshold value. Defaults to the dataset maximum. Ignored
          if ``hue`` is left unspecified.
      scale : str or iterable, optional
          Applies scaling to the output points. Defaults to None (no scaling).
      limits : (min, max) tuple, optional
          The minimum and maximum scale limits. Ignored if ``scale`` is left specified.
      scale_func : ufunc, optional
          The function used to scale point sizes. Defaults to a linear scale. For more information see `the Gallery demo
          <examples/usa-city-elevations.html>`_.
      legend : boolean, optional
          Whether or not to include a legend. Ignored if neither a ``hue`` nor a ``scale`` is specified.
      legend_values : list, optional
          The values to use in the legend. Defaults to equal intervals. For more information see `the Gallery demo
          <https://residentmario.github.io/geoplot/examples/largest-cities-usa.html>`_.
      legend_labels : list, optional
          The names to use in the legend. Defaults to the variable values. For more information see `the Gallery demo
          <https://residentmario.github.io/geoplot/examples/largest-cities-usa.html>`_.
      legend_var : "hue" or "scale", optional
          If both ``hue`` and ``scale`` are specified, which variable to use in the legend.
      legend_kwargs : dict, optional
          Keyword arguments to be passed to `the underlying legend <http://matplotlib.org/users/legend_guide.html>`_.
      extent : None or (minx, maxx, miny, maxy), optional
          Used to control plot x-axis and y-axis limits manually.
      figsize : tuple, optional
          An (x, y) tuple passed to ``matplotlib.figure`` which sets the size, in inches, of the resultant plot.
      ax : AxesSubplot or GeoAxesSubplot instance, optional
          A ``matplotlib.axes.AxesSubplot`` or ``cartopy.mpl.geoaxes.GeoAxesSubplot`` instance. Defaults to a new axis.
      kwargs: dict, optional
          Keyword arguments to be passed to the underlying `scatter plot
          <http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.scatter>`_.
  
      Returns
      -------
      ``AxesSubplot`` or ``GeoAxesSubplot``
          The plot axis
  
      Examples
      --------
  
      The ``pointplot`` is a `geospatial scatter plot <https://en.wikipedia.org/wiki/Scatter_plot>`_ representing
      each observation in your dataset with a single point. It is simple and easily interpretable plot that is nearly
      universally understood, making it an ideal choice for showing simple pointwise relationships between
      observations.
  
      The expected input is a ``GeoDataFrame`` containing geometries of the ``shapely.geometry.Point`` type. A
      bare-bones pointplot goes thusly:
  
      .. code-block:: python
  
          import geoplot as gplt
          import geoplot.crs as gcrs
          gplt.pointplot(points)
  
      .. image:: ../figures/pointplot/pointplot-initial.png
  
  
      The ``hue`` parameter accepts a data column and applies a colormap to the output. The ``legend`` parameter
      toggles a legend.
  
      .. code-block:: python
  
          gplt.pointplot(cities, projection=gcrs.AlbersEqualArea(), hue='ELEV_IN_FT', legend=True)
  
      .. image:: ../figures/pointplot/pointplot-legend.png
  
      The ``pointplot`` binning methodology is controlled using by `scheme`` parameter. The default is ``quantile``,
      which bins observations into classes of different sizes but the same numbers of observations. ``equal_interval``
      will creates bins that are the same size, but potentially containing different numbers of observations.
      The more complicated ``fisher_jenks`` scheme is an intermediate between the two.
  
      .. code-block:: python
  
          gplt.pointplot(cities, projection=gcrs.AlbersEqualArea(), hue='ELEV_IN_FT',
                         legend=True, scheme='equal_interval')
  
      .. image:: ../figures/pointplot/pointplot-scheme.png
  
      Alternatively, your data may already be `categorical
      <http://pandas.pydata.org/pandas-docs/stable/categorical.html>`_. In that case specify ``categorical=True`` instead.
  
      .. code-block:: python
  
          gplt.pointplot(collisions, projection=gcrs.AlbersEqualArea(), hue='BOROUGH',
                         legend=True, categorical=True)
  
      .. image:: ../figures/pointplot/pointplot-categorical.png
  
      Keyword arguments can be passed to the legend using the ``legend_kwargs`` argument. These arguments will be
      passed to the underlying ``matplotlib.legend.Legend`` instance (`ref
      <http://matplotlib.org/api/legend_api.html#matplotlib.legend.Legend>`_). The ``loc`` and ``bbox_to_anchor``
      parameters are particularly useful for positioning the legend. Other additional arguments will be passed to the
      underlying ``matplotlib`` `scatter plot <http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.scatter>`_.
  
      .. code-block:: python
  
          gplt.pointplot(collisions[collisions['BOROUGH'].notnull()], projection=gcrs.AlbersEqualArea(),
                         hue='BOROUGH', categorical=True,
                         legend=True, legend_kwargs={'loc': 'upper left'},
                         edgecolor='white', linewidth=0.5)
  
      .. image:: ../figures/pointplot/pointplot-kwargs.png
  
      Change the number of bins by specifying an alternative ``k`` value. Adjust the `colormap
      <http://matplotlib.org/examples/color/colormaps_reference.html>`_ using the ``cmap`` parameter. To use a
      continuous colormap, explicitly specify ``k=None``. Note that if ``legend=True``, a ``matplotlib``
      `colorbar legend <http://matplotlib.org/api/colorbar_api.html>`_ will be used.
  
      .. code-block:: python
  
          gplt.pointplot(data, projection=gcrs.AlbersEqualArea(),
                         hue='var', k=8,
                         edgecolor='white', linewidth=0.5,
                         legend=True, legend_kwargs={'bbox_to_anchor': (1.25, 1.0)})
  
      .. image:: ../figures/pointplot/pointplot-k.png
  
      ``scale`` provides an alternative or additional visual variable.
  
      .. code-block:: python
  
          gplt.pointplot(collisions, projection=gcrs.AlbersEqualArea(),
                         scale='NUMBER OF PERSONS INJURED',
                         legend=True, legend_kwargs={'loc': 'upper left'})
  
      .. image:: ../figures/pointplot/pointplot-scale.png
  
      The limits can be adjusted to fit your data using the ``limits`` parameter.
  
      .. code-block:: python
  
          gplt.pointplot(collisions, projection=gcrs.AlbersEqualArea(),
                         scale='NUMBER OF PERSONS INJURED', limits=(0, 10),
                         legend=True, legend_kwargs={'loc': 'upper left'})
  
      .. image:: ../figures/pointplot/pointplot-limits.png
  
      The default scaling function is linear: an observations at the midpoint of two others will be exactly midway
      between them in size. To specify an alternative scaling function, use the ``scale_func`` parameter. This should
      be a factory function of two variables which, when given the maximum and minimum of the dataset,
      returns a scaling function which will be applied to the rest of the data. A demo is available in
      the `example gallery <examples/usa-city-elevations.html>`_.
  
      .. code-block:: python
  
          def trivial_scale(minval, maxval):
              def scalar(val):
                  return 2
              return scalar
  
          gplt.pointplot(collisions, projection=gcrs.AlbersEqualArea(),
                         scale='NUMBER OF PERSONS INJURED', scale_func=trivial_scale,
                         legend=True, legend_kwargs={'loc': 'upper left'})
  
      .. image:: ../figures/pointplot/pointplot-scale-func.png
  
      ``hue`` and ``scale`` can co-exist. In case more than one visual variable is used, control which one appears in
      the legend using ``legend_var``.
  
      .. code-block:: python
  
          gplt.pointplot(collisions[collisions['BOROUGH'].notnull()],
                         projection=gcrs.AlbersEqualArea(),
                         hue='BOROUGH', categorical=True,
                         scale='NUMBER OF PERSONS INJURED', limits=(0, 10),
                         legend=True, legend_kwargs={'loc': 'upper left'},
                         legend_var='scale')
  
      .. image:: ../figures/pointplot/pointplot-legend-var.png
  
      """
      # Initialize the figure, if one hasn't been initialized already.
      fig = _init_figure(ax, figsize)
  
      xs = np.array([p.x for p in df.geometry])
      ys = np.array([p.y for p in df.geometry])
  
      if projection:
          # Properly set up the projection.
          projection = projection.load(df, {
              'central_longitude': lambda df: np.mean(np.array([p.x for p in df.geometry.centroid])),
              'central_latitude': lambda df: np.mean(np.array([p.y for p in df.geometry.centroid]))
          })
  
          # Set up the axis.
          if not ax:
              ax = plt.subplot(111, projection=projection)
  
          # Set extent.
          if extent:
              ax.set_extent(extent)
          else:
              pass  # Default extent.
      else:
          if not ax:
              ax = plt.gca()
  
      # Clean up patches.
      _lay_out_axes(ax, projection)
  
      # Immediately return if input geometry is empty.
      if len(df.geometry) == 0:
          return ax
  
      # Validate hue input.
      hue = _validate_hue(df, hue)
  
      # Set legend variable.
      if legend_var is None:
          if hue is not None:
              legend_var = "hue"
          elif scale is not None:
              legend_var = "scale"
  
      # Generate the coloring information, if needed. Follows one of two schemes, categorical or continuous,
      # based on whether or not ``k`` is specified (``hue`` must be specified for either to work).
      if k is not None:
          # Categorical colormap code path.
          categorical, k, scheme = _validate_buckets(categorical, k, scheme)
  
          if hue is not None:
              cmap, categories, hue_values = _discrete_colorize(categorical, hue, scheme, k, cmap, vmin, vmax)
              colors = [cmap.to_rgba(v) for v in hue_values]
  
              # Add a legend, if appropriate.
              if legend and (legend_var != "scale" or scale is None):
                  _paint_hue_legend(ax, categories, cmap, legend_labels, legend_kwargs)
          else:
              if 'color' not in kwargs.keys():
                  colors = ['steelblue']*len(df)
              else:
                  colors = [kwargs['color']]*len(df)
                  kwargs.pop('color')
      elif k is None and hue is not None:
          # Continuous colormap code path.
          hue_values = hue
          cmap = _continuous_colormap(hue_values, cmap, vmin, vmax)
          colors = [cmap.to_rgba(v) for v in hue_values]
  
          # Add a legend, if appropriate.
          if legend and (legend_var != "scale" or scale is None):
              _paint_colorbar_legend(ax, hue_values, cmap, legend_kwargs)
  
      # Check if the ``scale`` parameter is filled, and use it to fill a ``values`` name.
      if scale:
          if isinstance(scale, str):
              scalar_values = df[scale]
          else:
              scalar_values = scale
  
          # Compute a scale function.
          dmin, dmax = np.min(scalar_values), np.max(scalar_values)
          if not scale_func:
              dslope = (limits[1] - limits[0]) / (dmax - dmin)
              if np.isinf(dslope):  # Edge case: if dmax, dmin are <=10**-30 or so, will overflow and eval to infinity.
                  raise ValueError("The data range provided to the 'scale' variable is too small for the default "
                                   "scaling function. Normalize your data or provide a custom 'scale_func'.")
              dscale = lambda dval: limits[0] + dslope * (dval - dmin)
          else:
              dscale = scale_func(dmin, dmax)
  
          # Apply the scale function.
          scalar_multiples = np.array([dscale(d) for d in scalar_values])
          sizes = scalar_multiples * 20
  
          # When a scale is applied, large points will tend to obfuscate small ones. Bringing the smaller
          # points to the front (by plotting them last) is a necessary intermediate step, which is what this bit of
          # code does.
          sorted_indices = np.array(sorted(enumerate(sizes), key=lambda tup: tup[1])[::-1])[:,0].astype(int)
          xs = np.array(xs)[sorted_indices]
          ys = np.array(ys)[sorted_indices]
          sizes = np.array(sizes)[sorted_indices]
          colors = np.array(colors)[sorted_indices]
  
          # Draw a legend, if appropriate.
          if legend and (legend_var == "scale" or hue is None):
              _paint_carto_legend(ax, scalar_values, legend_values, legend_labels, dscale, legend_kwargs)
      else:
          sizes = kwargs.pop('s') if 's' in kwargs.keys() else 20
  
      # Draw.
      if projection:
          ax.scatter(xs, ys, transform=ccrs.PlateCarree(), c=colors, s=sizes, **kwargs)
      else:
          ax.scatter(xs, ys, c=colors, s=sizes, **kwargs)
  
      return ax